Find the unit tangent vector T(7) for the line tangent to the space curve r(t) = (12 cost, 12 sint, 3) at point P(6√√2,6√2,3).

Q: Determine which of the graphs below have Euler circuits. Vo Vg VI 3 m (US S 5 e6 4 33 V3 Ug (US 27…

A: Euler circuit: An Euler circuit starts & end at same Vertex Here in the given problem we have to…

Q: Evaluate x³ 2x² +7 dx S x² Ox² - 2x - 72 +0 0²-2x - 1 + C X O2+2 +c+C -2+7ln x² + C -

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Q: Find the area of the shaded region. r = 1 + cos 0

A: Here, the given curves are r=1+cos θ & r=3 cos θ First of all find the intersection points of…

Q: At point (1,-1,2). 4

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Q: Q6A)If y sin find Zxy.

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Q: The total cost (in dollars) of producing x food processors is C(x) = 1600+50x-0.4x². Find the…

A: Derivative of total cost function gives the marginal cost function

Q: f 2³x dx = O 0 23x In 2 + C ○ 23x+1 + C 3x+1 23x In 8 0 23x ln 2 O + C + C

A: To evaluate: I=∫23xdx

Q: Find area bounded by y = 0, y = √x - x² using double integration.

A: Graph: Now, we need to find the area of the above figure.

Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i - 3j-k, find vector normal to A and In plane of A and, B.…

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Q: Find the interval of convergence of the power series: ∞ n [²(+1²] (x + 1)n 1)"] 2n n=0

A: To find the interval of convergence.

Q: sint do соби Ө

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Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

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Q: Let one week's supply and demand functions for gasoline be given by p= D(q) = 288-39 and p = S(q) =…

A: Here, the demand and supply functions are: D(q)=288-43q & S(q)=23q which are the linear…

Q: Solve differential equation dy dx -(x²+y) x+siny

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Q: use the chain rule to find the derivative of function 3 5t² 3t²+2

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Q: Please determine if the sequence converges or diverges. \left(\frac{n!+6}{n!-2}\right)

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Q: cos(In2x) X A) cos(Inx) + c C) sin(In2x) + c dx = ? B) sin(Inx) + c D) E) 2.sin(In2x) + c 2…

A: Given

Q: If f³ f (x) dx = 6 and ſ ƒ(x)dx = 4, then ſ5 (3 + 2ƒ(x))dx : = 35 10 23 20

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Q: Question 6 Given: f (x, y, z) = cos(xyz) + ln x5 - sinh y² + 3z Find: af(x, y, z) дz at P(-1, 3, 0)…

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Q: Select all of the following tables which represent y as a function of x. X Y Y X y X Y -3 -2 -3 -4…

A: Explained below

Q: At which value of x is the function whose graph is shown below differentiable? 8 N 4 -2 0 2 4 6 -8…

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Q: 4. When finding the derivative of a fraction you have to use the Quotient Rule. 5. The derivative of…

A: 4. when finding the derivative of a fraction you have to use the quotient rule.5. The derivative of…

Q: Evaluate lim x - 4 3 O O 3 1. 4 3 2 3 (2x + 1)² 3x² + 8x - 3

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Q: Using the definition of the derivative, find f'(x). Then find f'(1), f'(2), and f'(3) when the…

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Q: 7 For the graph represented by the drawing below, find all edges that are incident on v1.

A: FOR the graph represented by drawing below ,find all the edges that are incident on V1

Q: A particle moves in the yz-plane along the curve represented by the vector-valued function r(t) = (4…

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Q: Solve using Inverse Operaators. y"" - y = 4e-x + 3e2x; Particular Solution: Y=C1+ C₂ eax + C3 ebx…

A: Given that,

Q: dy -(x²+y) B)Solve differential equation = dx x+siny

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Q: Find the slope of the tangent line to the graph of the given function at the given value of x. 1/2…

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Q: Suppose that the total profit function for a company is given by P(x) = 4x³ - 210x² + 3600x - 200,…

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Q: The area enclosed by the two curves y = x² - 4 and y = x - 4 is given by. a. f(x-x²) dx b. (x²-x) dx…

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Q: Find the equation of the line tangent to the graph of f(x) = ₂ at x = 3.

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Q: B)Evaluate the integrals: i) f/2 inzerdrde " 0 ii) f/25/2 sinx 2² siny dz dy dx. π/2

A: B.1. According to question,Given Integral,Let I = ∫0π2∫0sin 2θr dr dθ

Q: Find both first partial derivatives. z = 8y2 sqaureroot x

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Q: a) y || (т. 3x 5x-x2 3

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Q: Evaluate f(2x² + 3x + 1)5 (8x + 6) dx

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Q: ror(4)). 95. Find the restrictions in the domain, if any, for If there is more than one restriction,…

A: Note: The first question that is question 90 seems incomplete. So, solving 95 for you.

Q: Given : y = cot √2x + 1 Find dy dx O csc² √2x + 1 √2x+1 O csc² √2x + 1 2√2x+1

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Q: Sketch the graph off and use your sketch to find the absolute and local maximum and minimum values…

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Q: Fill in the blanks: Use integration to find the volume of the solid obtained by revolving the region…

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Q: Given that f(x) = (x - 6)² and g(x) = 1 and g(x) = 1 – 2x, find

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Q: A conical vessel 12m across the top and 15m deep. If it contains water to a depth of 10m, find the…

A: Concept: Similar triangles are those which are of the same shape but need not be of the same size…

Q: Evaluate 3+x lim,¬4¹ (x-4)(x+2) 01 0 0 8-8 O +∞

A: The given limit is: limx→4+3+xx-4x+2

Q: The y-intercept of the parabola y = - (x-20)^2 + 100 is

A: The given equation of the parabola is: y=-x-202+100   As we know that; To determine y-intercept, we…

Q: c. Given f(x) = 2x - 3, g(x) = -4x² +9, h(x) = 4x² - 12x +9; find f(x)* g(x) 2. h(x)/ f(x) 3.…

A: Given, f(x) =(2x-3) g(x) = -4x2+9 = 9-4x2 = (3)2-(2x)2 = (3-2x)(3+2x)  h(x) = 4x2-12x+9 =…

Q: 17 What is the degree of vertex 4? O 1 ez el V2 V₂ Des

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Q: 5. Find the general solution of the differential equation using GeoGebra (D² +9)y=2 sina

A: General equation of differential equation.

Q: Use cylindrical coordinates. Find the volume of the solid that lies within both the cylinder x² + y²…

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Q: Determine the Cartesian equation of a plane that is perpendicular to the plane x - 2y + z = 6 and…

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Q: Suppose that the total profit function for a company is given by P(x) = 4x³ - 210x² + 3600x - 200,…

A: We have to choose correct option for given questions.